The shape and the fabric of human cultural history is the focus of two long-standing debates in linguistics and anthropology. The first concerns the extent to which human history is tree-like (its shape), and the second concerns the unity of that history (its fabric). Proponents of cultural phylogenetics are often accused of assuming that human history has been both highly tree-like and consisting of tightly linked lineages. Critics have pointed out obvious exceptions to these assumptions. Instead of a priori dichotomous disputes about the validity of cultural phylogenetics, we suggest that the debate is better conceptualized as involving positions along continuous dimensions. The challenge for empirical research is, therefore, to determine where particular aspects of culture lie on these dimensions. We discuss the ability of current computational methods derived from evolutionary biology to address these questions. These methods are then used to compare the extent to which lexical evolution is tree-like in different parts of the world and to evaluate the coherence of cultural and linguistic lineages.